Visualizing Distribution Coverage in Diffusion Models

Modern diffusion pipelines rely on distribution-shaping and acceleration techniques such as classifier-free guidance, few-step distillation, and video forcing. However, improvements in sample quality do not reveal how these interventions reshape distribution coverage. We study this question through pass@$k$, a sampling-budget lens on distribution coverage. Pass@$1$ reports mean one-draw success, whereas the pass@$k$ curve provides nonlinear summaries of how prompt-wise success probabilities are distributed and whether an early advantage persists as additional samples are drawn. Using CFG as a controlled proof of concept, we find that high guidance improves pass@$1$, but its advantage shrinks and can reverse at larger $k$. Across few-step diffusion families, several students similarly lead at small budgets but trail their multi-step teachers at larger budgets. A controlled ablation reveals an objective-level divide: distribution-matching distillation improves early-hit performance by concentrating the output distribution but systematically reduces large-budget distribution coverage, whereas consistency-style distillation better preserves coverage. Finally, video-forcing recipes exhibit different marginal best-of-$k$ gains as the sampling budget increases, extending the same analysis to video generation. Together, these results establish pass@$k$ as a practical diagnostic of distribution coverage in diffusion model generations.